Color and Spectra

In this experiment we used a diffraction gradient to measure the spectral lines of a white light source and that given off by an unknown gas. The purpose of the first part of this experiment is to make sure that we have to appropriate setup and that we can me accurate measurements with our apparatus. In the second part of the experiment we will measure the spectral line spacing and record their color. We would then match these lines with known spectral lines a sever different elements and determine what was our unknown gas.

To begin the experiment would first take a two meter long ruler and place it perpendicular to a one meter long ruler so that the two rulers formed an "L" shape. Where the two ruler met we placed our light source. At the opposite end of two meter long ruler we placed our diffraction gradient. We were careful to make it so the light source sat right at the end of the ruler so that the diffraction gradient was exactly two meters away (within uncertainty). In a dark room we turned on our light source and looked trough the diffraction gradient. We then made measurements where the visual spectrum laid along the one meter long ruler for the white light source. For the unknown gas we did the same except we noted where the spectral lines fell along the one meter long ruler and their color. The setup with the unknown gas is shown below.

In this experiment we will be using the equation (lambda)=(D*d)/[sqrt(L^2+D^2)] where lambda is our wavelength, L is 2 meters, D is the distance along the one meter ruler we will be recording, and d is the slit spacing in the diffraction gradient which is 1.67*10^-6 meters.

For the first part of the experiment were we used the light bulb we measured the length of the spectrum and where we saw the colors red, yellow, green, blue, and violet. We then got the following values. All measurements have an uncertainty of +/- 0.005 meters
Violet: 0.435 m
Blue: 0.495 m
Green: 0.585 m
Yellow: 0.65 m
Red 0.76 m
The entire visible spectrum ranged from 0.42 m to 0.855 m. Using the above equation we find that our spectrum ranged from 341 nm to 652 nm. The true visual spectrum ranges from about 380 nm to 750 nm. This indicates that our spectrum has been shifted to the left and compressed slightly. We will later plot a graph and use an equation to account for this.

In the next part of our experiment we replaced the light with a tube filled with an unknown  gas. A large voltage is run across the tube which allows it to glow. We then looked through the diffraction gradient and measured the spectral lines. The values are below with uncertainties of +/-0.0025 m
Violet: 0.5225 m
Green: 0.6075 m
Yellow: 0.645 m
Red: 0.665 m
Using the above equation we found the wavelength at each of our lines. All values have an uncertainty of +/-4nm
Violet: 422nm
Green: 485nm
Yellow: 513nm
Red: 642nm
Using a chart with spectral lines of known gases we compared the spectral lines of our unknown gas. We then determined that our lines most closely resembled the lines in mercury.

To help correct our values we then looked at the spectral lines of hydrogen and made our measurements. Hydrogen was used because it has fewer spectral lines and a plot could be graphed that corrected for the shift in the previous sections of the experiment. We obtained the following values for hydrogen.
Violet/Blue: 0.465 m
Green: 0.506 m
Orange/Yellow: 0.621 m
Red: 0.708 m
The corresponding wavelengths are as follows. All values have an uncertainty of +/- 11nm
Violet/Blue: 378 nm
Green: 410 nm
Orange/Yellow: 495 nm
Red: 557 nm
After plotting the values into excel we plotted our data to give us our correction factor which resulted in the equation (lambda)_actual=1.051*(lambda_exp)+4.538. Using this equation we were given our corrected wavelengths. All the values have an uncertainty of +/- 16 nm.
Violet/Blue: 402nm
Green: 435nm
Orange/Yellow: 525nm
Red: 590nm

After the calibration we found that  our results were fairly close to the true values for each of the corresponding colors with the largest percent difference being 5%. This falls well within our range of uncertainty and can be accounted for by the uncertainty of our measurements.